Monday, July 21, 2008

Top 20 On/Off Ice Adjusted +/- Ratings

My first attempt to address the sabermetrics and hockey problem of rating individual player's defensively is to look at +/- ratings adjusted to give the difference between +/- when a player is on the ice and off the ice per sixty minutes played (which is an idea popularized by behind the net). The top players will not necessarily be the top defensive players in the league. They are merely players who had their team do better (in terms of goals for and against) when they are on the ice when compared to when they are not. Thus these players might be offensive stars. These players might be players who were used in special situations (for example with top linemates or against weak opposition) that allowed them their success in this statistic. These players are all players who excelled in the role they played on their team. Those players on this list who are star players on their team are some of the best players in the league. The lesser known players generally excelled in their lesser roles and probably are able to handle increased responsibility in the future in their career.

I wouldn't put too much importance on the exact order of players on this list, as it is at best a weak correlation between a player being on the ice and his team scoring or allowing a goal in many cases. Often goals are scored when a player in not directly involved in the play. It is very easy to imagine any player's totals being shifted by five or more goals (this is less than one per month of the regular season) merely by chance. That kind of uncertainty on these calculations would be able to shift the order of the top twenty players in this adjusted +/- list significantly. What is important is which players are present. They are players who excelled in their roles with their teams last season. It gives us a glimpse at defence because there are players on this list who are not high scoring; they must have made this list with good defence. However, it is an incorrect interpretation to suggest that these players are the best defensive players in the NHL last year.

In order to have played enough for their numbers to be meaningful, I have limited this list to the 525 players (non-goalies) who played 50 or more games played in the 2007/08 season.

Top 20 On/Off Ice Adjusted +/- Ratings 2007/08

Rank

Player

Team

On Ice +/-

Off Ice +/-

Adjusted +/-

1

David Perron

StL

+1.67

-0.62

2.29

2

Dany Heatley

Ott

+1.68

-0.48

2.16

3

Viktor Kozlov

Was

+1.56

-0.60

2.16

4

Michel Ouellet

TB

+0.96

-1.19

2.15

5

Pavel Datsyuk

Det

+2.20

+0.15

2.05

6

Paul Stastny

Col

+1.66

-0.34

2.00

7

Ryan Getzlaf

Ana

+1.60

-0.32

1.92

8

Jarome Iginla

Cal

+1.47

-0.43

1.90

9

Jason Arnott

Nas

+1.43

-0.47

1.90

10

Joe Thornton

SJ

+1.35

-0.54

1.89

11

Milan Michalek

SJ

+1.34

-0.55

1.89

12

Jason Spezza

Ott

+1.39

-0.46

1.85

13

Henrik Zetterberg

Det

+1.89

+0.08

1.81

14

Sidney Crosby

Pit

+1.41

-0.38

1.79

15

Johnny Oduya

NJ

+1.28

-0.48

1.76

16

Alexander Ovechkin

Was

+1.23

-0.51

1.74

17

Nicklas Lidstrom

Det

+1.92

+0.26

1.66

18

Shawn Horcoff

Edm

+0.47

-1.19

1.66

19

Mats Sundin

Tor

+1.05

-0.55

1.60

20

David Booth

Flo

+0.92

-0.66

1.58

We see David Perron as a surprise leader of this list. Perron was far from the best player in the NHL last season. But he excelled in a protected role with the St Louis Blues playing against weak opposition. Perron is ready to make a big step forward this season.

Next up is Dany Heatley of the Ottawa Senators, who is a very good two-way player and one of the better players in the NHL.

Third is Viktor Kozlov. I think it is likely a statistical fluke that he ranks ahead of teammate Alexander Ovechkin, though he does. He is a better two-way player than he gets credit for.

Next up is Michel Ouellet, who excelled in a sheltered role in Tampa where he was played against weaker opposition. It will be interesting to see where he fits on the team next year now that they have added several new forwards.

The next three players are stars who play very good two-way games in Selke Trophy winning Pavel Datsyuk, Paul Stastny and Ryan Getzlaf.

Next up are further players who were the stars on their teams in Jarome Iginla, the under-rated Jason Arnott and Joe Thornton.

Milan Michalek comes along with Joe Thornton in San Jose. They were linemates and usually played under the same circumstances.

Next up are NHL stars Jason Spezza, Henrik Zetterberg and Sidney Crosby.

Next up comes the top defenceman on the list (probably defenceman play in such a wide range of situations that it is hard to crack such a list) Johnny Oduya of the New Jersey Devils, who I called the NHL's most unsung hero.

He is followed by MVP Alexander Ovechkin and Norris Trophy winner Nicklas Lidstrom (the second defenceman on this list).

Next up are two players who were the stars on teams that missed the playoffs. They are Shawn Horcoff of the Edmonton Oilers and Mats Sundin, who last year was a Toronto Maple Leaf.
The final player on the list played successfully against weak opposition. David Booth in Florida. He is ready for a bigger role next season.

This list is a list of twenty good NHL players who excelled in their roles last season. All are solid defensively, though they are not the twenty best defensive players in the league by any reasonable measure.

Adjusting +/- ratings for on and off ice rates is a useful method to identify some very good hockey players. These players are all responsible defensively, but this does not isolate defensive play. A player can make this list by being a top scorer. It is a start in finding good defensive players in the NHL. Players like Jason Arnott, Johnny Oduya and David Perron are among those isolated. They are on this list with well known NHL stars like Alexander Ovechkin, Sidney Crosby and Jarome Iginla. You wouldn't go wrong with any of these players on your team, but more work must be done to try to isolate defensive ability. This step starts down that path, but is a long way from completing the job.

This actually measures players who are significantly more effective at even-strength than their *teammates*, but not really the best of the league. Measuring "on-stats" against "off-stats" is very useful to measure the relative importance of a player to his team, but comparisons between players on different teams are going to be inherently flawed. It is dependent not only on the quality of linemates and opposition, like straight +/- is, but also the quality of those teammates who don't play when you do; it actually penalizes players for being on a good team and rewards top performers on worse teams. It also punishes you doubly if you face tough opposition, because it not only lowers your personal +/-, it also improves the rest of the teams' +/- since they get softer minutes as they don't have to face the tough minutes you're getting.

For example, Shawn Horcoff is on this list more because his teammates proved inept 5-on-5 than because he himself was a great 5-on-5 player. Transplant him on a team with better +/- overall and he might not make the list at all, even though his personal +/- may well increase as a result of better teammates.

Meanwhile, Datsyuk and Zetterberg show well on this list, but it would be even higher if the rest of their team's +/- was not so high. It does tell us something interesting though: how much Detroit's 5-on-5 success actually depends on these two guys.

The raw info needed to calculate this is fouind on behind the net. I plan to look at some more results from that site in the future.

Mathman

Obviously when you normalize something there will be some question about how to normalize it. I think the assumptions that go with normalizing +/- to a team's result when a player is not on the ice are pretty good for the current NHL. That will give the best results in a parity-filled NHL, where all teams are essentially the same, which is a good approximation for the NHL of today.

Obviously, it will fail in some limits. If all these 20 players were teammates, they could not all be the top 20 adjusted +/- ratings. If we had a team that was made up of one NHL superstar and a bunch of chimpanzees, the effect of the one superstar to his team would be tremendous and it would look bigger because it is being compared to a group that cannot play hockey. But I agrue neither of these cases exist in the NHL today.

A quick test to show that this isn't a bad normalization is that 15 of the 20 players on the top 20 list made the playoffs. If it was a truly random assortment of players from all teams, one would expect 10.67 players (16/30*20) from playoff teams. We are well ahead of that number, which is expected as good teams tend to have good players (thats why they are good). I wouldn't argue that there is a bias to incölude players from bad teams when players from bad teams are under-represented when compared to a random assortment of players.

If the best example of a player making this list from a bad team is Shawn Horcoff (and he is that best example - nobody in the NHL had a worse off ice +/- than Horcoff did) and he comes from a team that finished in 19th place (only 3 points out of the playoffs) as opposed to a team that was truly a last place team, it does a very good job of supporting the parity model of the NHL. This also shows the importance of Shawn Horcoff to the Oilers. I think it is a bigger impact than most recognize. It may also show that the Oilers were not as good as their record showed (due in part to shootout success inflating the record), but for the most part, it shows this is not a bad normalization.

Of course there are many ways to normalize things. If time permits this summer, I would like to look at another method. Given how weak the correlation between being on the ice for a goal and the talent level of an individual player, you would expect some problems may exist in trying to find a way to compare these kinds of numbers between different teams, but this is a good and useful start. Obviously, it can be pushed too far. Small numerical differences are probably error. It is the larger numerical differences that are sigfnificant and they can sometimes be (partially) explained by the circumsatces under which a player plays. Like all numbers, you have to take these with a grain of salt, but I argue that they are useful. This list is a group of players who played well last year in the roles they were given.